Quasi-Transfer Continuity and Nash Equilibrium

2019 ◽  
Vol 21 (04) ◽  
pp. 1950004
Author(s):  
Rabia Nessah ◽  
Tarik Tazdait
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Existence Result ◽  
Mixed Strategy ◽  
Existence Theorems ◽  
Pure Strategy ◽  
Econ Theory ◽  
Discontinuous Games ◽  
Normal Form Games ◽  
Existence Of Equilibria

We introduce a new notion of continuity, called quasi-transfer continuity, and show that it is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. This holds true in a large class of discontinuous games. We show that our result strictly generalizes the pure strategy existence theorem of Carmona [Carmona, G. [2009] An existence result for discontinuous games, J. Econ. Theory 144, 1333–1340]. We also show that our result is neither implied by nor does it imply the existence theorems of Reny [Reny, J. P. [1999] On the existence of pure and mixed strategy Nash equilibria in discontinuous games, Econometrica 67, 1029–1056] and Baye et al. [Baye, M. R., Tian, G. and Zhou, J. [1993] Characterizations of the existence of equilibria in games with discontinuous and nonquasiconcave payoffs, Rev. Econ. Studies 60, 935–948].

scholarly journals Learning Deviation Payoffs in Simulation-Based Games

2019 ◽  
Vol 33 ◽  
pp. 2173-2180 ◽  
Author(s):  
Samuel Sokota ◽  
Caleb Ho ◽  
Bryce Wiedenbeck
Keyword(s):  
Neural Networks ◽  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Mixed Strategy ◽  
State Of The Art ◽  
Pure Strategy ◽  
Normal Form Games ◽  
Novel Approach ◽  
Simulation Based ◽  
Expected Values

We present a novel approach for identifying approximate role-symmetric Nash equilibria in large simulation-based games. Our method uses neural networks to learn a mapping from mixed-strategy profiles to deviation payoffs—the expected values of playing pure-strategy deviations from those profiles. This learning can generalize from data about a tiny fraction of a game’s outcomes, permitting tractable analysis of exponentially large normal-form games. We give a procedure for iteratively refining the learned model with new data produced by sampling in the neighborhood of each candidate Nash equilibrium. Relative to the existing state of the art, deviation payoff learning dramatically simplifies the task of computing equilibria and more effectively addresses player asymmetries. We demonstrate empirically that deviation payoff learning identifies better approximate equilibria than previous methods and can handle more difficult settings, including games with many more players, strategies, and roles.

On the Existence of Pareto Efficient Nash Equilibria in Discontinuous Games

2017 ◽  
Vol 19 (03) ◽  
pp. 1750014
Author(s):  
Rabia Nessah ◽  
Raluca Parvulescu
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Existence Theorems ◽  
Compact Convex ◽  
Existence Results ◽  
Discontinuous Games ◽  
Pareto Efficient

This paper gives existence theorems of pure, Pareto efficient, Nash equilibrium in compact, convex and discontinuous games. These conditions are simple and straightforward to verify. Moreover, the present existence results neither imply nor are implied by the known results in the literature. The results are illustrated by several examples.

Nash Equilibrium in Discontinuous Games

2020 ◽  
Vol 12 (1) ◽  
pp. 439-470
Author(s):  
Philip J. Reny
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Mixed Strategy ◽  
Discontinuous Games ◽  
Bayesian Games ◽  
Sharp Focus

We review the discontinuous games literature, with a sharp focus on conditions that ensure the existence of pure and mixed strategy Nash equilibria in strategic form games and of Bayes-Nash equilibria in Bayesian games.

scholarly journals Representing pure Nash equilibria in argumentation

2021 ◽  
pp. 1-14
Author(s):  
Bruno Yun ◽  
Srdjan Vesic ◽  
Nir Oren
Keyword(s):  
Normal Form ◽  
Nash Equilibria ◽  
Pure Strategy ◽  
Normal Form Games

In this paper we describe an argumentation-based representation of normal form games, and demonstrate how argumentation can be used to compute pure strategy Nash equilibria. Our approach builds on Modgil’s Extended Argumentation Frameworks. We demonstrate its correctness, showprove several theoretical properties it satisfies, and outline how it can be used to explain why certain strategies are Nash equilibria to a non-expert human user.

On the Foundations of Nash Equilibrium

1996 ◽  
Vol 12 (1) ◽  
pp. 67-88 ◽  
Author(s):  
Hans Jørgen Jacobsen
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Cooperative Game Theory ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Mixed Strategies ◽  
Positive Theory ◽  
Equilibrium Concept ◽  
Strategy Equilibrium ◽  
Pure Strategies

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.

scholarly journals A Note on Anti-Berge Equilibrium for Bimatrix Game

2021 ◽  
Vol 36 ◽  
pp. 3-13
Author(s):  
R. Enkhbat ◽  
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Differential Games ◽  
Search Algorithm ◽  
Existence Theorems ◽  
Applied Mathematics ◽  
Pure Strategy ◽  
Bimatrix Game ◽  
French Mathematician ◽  
Berge Equilibrium

Game theory plays an important role in applied mathematics, economics and decision theory. There are many works devoted to game theory. Most of them deals with a Nash equilibrium. A global search algorithm for finding a Nash equilibrium was proposed in [13]. Also, the extraproximal and extragradient algorithms for the Nash equilibrium have been discussed in [3]. Berge equilibrium is a model of cooperation in social dilemmas, including the Prisoner’s Dilemma games [15]. The Berge equilibrium concept was introduced by the French mathematician Claude Berge [5] for coalition games. The first research works of Berge equilibrium were conducted by Vaisman and Zhukovskiy [18; 19]. A method for constructing a Berge equilibrium which is Pareto-maximal with respect to all other Berge equilibriums has been examined in Zhukovskiy [10]. Also, the equilibrium was studied in [16] from a view point of differential games. Abalo and Kostreva [1; 2] proved the existence theorems for pure-strategy Berge equilibrium in strategic-form games of differential games. Nessah [11] and Larbani, Tazdait [12] provided with a new existence theorem. Applications of Berge equilibrium in social science have been discussed in [6; 17]. Also, the work [7] deals with an application of Berge equilibrium in economics. Connection of Nash and Berge equilibriums has been shown in [17]. Most recently, the Berge equilibrium was examined in Enkhbat and Batbileg [14] for Bimatrix game with its nonconvex optimization reduction. In this paper, inspired by Nash and Berge equilibriums, we introduce a new notion of equilibrium so-called Anti-Berge equilibrium. The main goal of this paper is to examine Anti-Berge equilibrium for bimatrix game. The work is organized as follows. Section 2 is devoted to the existence of Anti-Berge equilibrium in a bimatrix game for mixed strategies. In Section 3, an optimization formulation of Anti-Berge equilibrium has been formulated.

scholarly journals Strict pure strategy Nash equilibria in large finite‐player games

2021 ◽  
Vol 16 (3) ◽  
pp. 1055-1093
Author(s):  
Guilherme Carmona ◽  
Konrad Podczeck
Keyword(s):  
Nash Equilibria ◽  
Existence Result ◽  
Pure Strategy ◽  
The Other ◽  
Precise Sense ◽  
Equilibrium Distributions ◽  
Payoff Functions ◽  
Anonymous Games ◽  
Differentiability Properties

In the context of anonymous games (i.e., games where the payoff of a player is, apart from his/her own action, determined by the distribution of the actions made by the other players), we present a model in which, generically (in a precise sense), finite‐player games have strict pure strategy Nash equilibria if the number of agents is large. A key feature of our model is that payoff functions have differentiability properties. A consequence of our existence result is that, in our model, equilibrium distributions of non‐atomic games are asymptotically implementable by pure strategy Nash equilibria of large finite‐player games.

Sign in / Sign up

Export Citation Format

Share Document